Since the corrosion will have traveled up the wire, the only cure is to "mend it with a new one". Having less and less metal in the lead over time will have restricted the battery's current delivery capability, and the battery might well be a good way along its natural lifespan anyway, so a new lead will certainly improve matters, but might not reset performance back to day one.
I have in the past tried reconnecting such wires, stripping back the insulation and cleaning the corrosion off. This invariably just leaves a pile of bits of thin wire because the surface corrosion has gone most of the way through each strand. Repeating the process takes you far enough along to convince you that it is an exercise in futility.
Stopping it happening again is mostly a matter of sealing the ends so that air (especially damp air) cannot get in, but if the new wire lasts as long as the old one, this might not be a real concern. Any sealing obviously needs to happen after the soldering.